This line 

> The symbol may naturally be thought of as an element in the K-theory
> of X

appears in the [nLab page on principal symbols][1] for differential operators. What does this mean? Are they talking about K-theory or K-homology? How does one produce a class from the symbol of the operator?


  [1]: https://ncatlab.org/nlab/show/symbol+of+a+differential+operator